Trigonometry

Section 1: Trigonometric Functions and Identities

Proof of Trigonometric Identities

Look at this right-angled triangle.

Its hypotenuse is 1 unit long. It is placed inside a unit circle. So we can define:-

sin1y y= = 1

cos1x x= = 2

O

P (x, y)

x

1

x

y

y

tan yx

= 3

Substituting 1 and 2 into 3 we get: sintancos

By Pythagoras Theorem on the right angled triangle:

2 2 1y x+ = 4 Substituting 1 and 2 into 4 we get: 2 2sin cos 1 + 5

MEI, 12/04/05 1/1